The present invention relates to magnetic resonance imaging and, more particularly, to a method of filtering noise from magnetic resonance images.
In the last decade Magnetic Resonance Imaging (MRI) has become a standard diagnostic imaging modality, that offers, for a full host of applications, high temporal and spatial resolution images that surpass in their quality those provided by other imaging techniques. Because of the high cost of MRI machine time and because of patient discomfort staying in the magnet for a long time, any reduction in acquisition time without compromising image quality is valuable. In order to improve data quality, one would like to increase the temporal and spatial resolutions beyond those achieved in the raw data.
The signal-to-noise ratio of MRI data has always been the limiting factor for higher spatial and temporal resolutions. Theoretically, the intrinsic spatial and temporal resolutions, constrained by the water apparent diffusion constants, are of the order of magnitude of a few microns and a few milliseconds. Practically however, the system's gradients strength and their rise time define the maximum resolution available in the data. With the constant improvement of these two parameters, the operative limit to the resolution is determined by the image signal-to-noise ratio. Because of the averaging procedure applied to the data, there is a trade off between the spatial resolution and the temporal resolution of the image.
In the emerging field of functional MRI to study the human brain, improving the signal-to-noise ratio is even more important. In these studies, high temporal resolution is desired, which makes a signal averaging procedure improper.
Recovery of an image from noisy MR data is a classic problem of inversion. A straightforward inversion often is unstable and a regularization or image processing scheme of some sort, in order to interpolate where data are noisy, is essential. Image processing spans a variety of methods, starting from the classical, e.g. Wiener filtering and Principal Component Analysis, to the more modem, and usually non-linear, methods, such as Artificial Neural Networks, Maximum-Entropy, and Wavelets analysis. All of these methods attempt, subject to some assumptions, to extract the maximum amount of "useful" information content from the image.
In many of those methods the data are expanded in some functional basis that maintains their phase distribution as well as their power spread over various scales, i.e. power spectrum. With a clever choice of functional basis, it often is possible to distinguish between the various contributions to MRI data. Such a distinction facilitates filtering of undesired contributions, e.g. noise.
During the last decade wavelets have become a popular tool in various data analysis and signal and image processing applications. Wavelet functional bases' main appeal stems from their simultaneous localization in both the wavenumber (frequency) and the position (time) domains, where they allow for an orthogonal and complete projection on modes localized in both physical and transform spaces, therefore make possible a multi-resolution analysis of images. The localization allows for compressing the noiseless image features into a very small number of very large wavelet coefficients. Gaussian white noise, however, stays as white noise in any orthogonal basis, therefore spreading in wavelet space over all expansion coefficients and contributing to each of them a relatively small amplitude. Consequently, in a wavelet basis, the noiseless signal dominated coefficients can be easily singled out from their noise dominated counterparts.
In summary, decomposition via wavelets has two main advantages: First, it maintains spatial (temporal) as well as characteristic wavenumber (frequency) information. Second, many classes of functions can be expanded in a relatively small number of wavelet basis functions while keeping most of their information content. These two properties make wavelets an excellent tool for noise filtering and data compression A particularly popular class of wavelet functional bases is the computationally efficient, discrete wavelet transforms (DWT).